On the local structure of Hecke O G-interior algebras

Abstract

Keep all the notation of Section 4, set

$${A^{..}} = Ind_{{H^{..}}}^{G \times G'}\left( {{B^{..}}} \right)and\,\hat A = Ind_{{H^{..}}}^{G \times G'}{\left( {{B^{..}}} \right)^{1 \times G'}}$$

(5.1.1)

and consider a point â of G on Â; in this section we determine a defect pointed group of G _â and the corresponding source algebra and multiplicity module (cf. 2.8 and 2.9), from analogous local invariants of B ^... This knowledge of the local structure of the Hecke OG-interior algebra  will be enough to study Morita equivalences between blocks, and we postpone the systematic analysis of the local pointed groups on  until Section 16, in order to do it in the more general framework of the D G-interior algebras, except for the contents of Proposition 5.5 and Corollary 5.7 below which will apply to D G-interior algebras as it stands.